Find a polar equation for the curve represented by the given Cartesian equation. y = 1 + 3x

Solution:

Given cartesian equation y = 1 + 3x

We can easily convert equations from cartesian coordinates to polar coordinates by making the substitutions.

 x = rcos(θ) and y = rsin(θ)

Therefore, the equation y = 1 + 3x will be rewritten as rsin(θ) = 1 + 3(rcos(θ))

Hence, we can write y = 1 + 3x as rsin(θ) = 1 + 3rcos(θ)

Therefore, the polar equation for y = 1 + 3x is rsin(θ) = 1 + 3rcos(θ)

Find a polar equation for the curve represented by the given Cartesian equation. y = 1 + 3x

Summary:

The polar equation for the curve represented by the given Cartesian equation. y = 1 + 3x is rsin(θ) = 1 + 3rcos(θ)